Group-III-element nitride semiconductors are used in the fields of, for instance, hetero-junction high-speed electron devices and photoelectron devices (such as laser diodes, light-emitting diodes, sensors, etc). Particularly, gallium nitride (GaN) has been gaining attention. Conventionally, in order to obtain single crystals of gallium nitride, gallium and nitrogen gas are allowed to react with each other directly (see J. Phys. Chem. Solids, 1995, 56, 639). In this case, however, ultrahigh temperature and pressure, specifically 1300° C. to 1600° C. and 8000 atm to 17000 atm (0.81 MPa to 1.72 MPa) are required. In order to solve this problem, a technique of growing gallium nitride single crystals in a sodium (Na) flux (hereinafter also referred to as a “Na flux method”) has been developed (see, for instance, U.S. Pat. No. 5,868,837). This method allows the heating temperature to be decreased considerably to 600° C. to 800° C. and also allows the pressure to be decreased down to about 50 atm (about 5 MPa). In this method, however, the resulting single crystals are blackened and there therefore is a problem of quality. Furthermore, the conventional techniques do not make it possible to produce gallium nitride single crystals that have a lower dislocation density and a uniform thickness (i.e. a substantially level crystal surface) and are transparent, high quality, large, and bulk crystals. In addition, the conventional techniques have a lower yield. That is, in the conventional techniques, the growth rate is particularly low, and even the largest diameter of the largest gallium nitride single crystals that have been reported until now is about 1 cm, which does not allow gallium nitride to be used practically. For instance, a method has been reported in which lithium nitride (Li3N) and gallium are allowed to react with each other to grow gallium nitride single crystals (see Journal of Crystal Growth 247(2003)275-278). However, the size of the crystals obtained using the method was only about 1 mm to 4 mm. These problems are not peculiar to gallium nitride. The same applies to semiconductors of other Group-III-element nitrides.